Acceleration, Ratio. Quotient

Though ratios are mathematically represented as quotients, there are important distinctions between the two relations.  First, 'is proportionate to', but not 'divided by', is a symmetrical relation.  Second, a ratio, unlike a quotient, does not reduce to a single numerical value, which means that a quotient with a ratio as either divisor or dividend is ill-formed.  Nevertheless, the standard Physics representation of Acceleration suppresses both these distinctions, beginning with its representation, as a quotient, Velocity, which, fundamentally is a ratio between measured Distance and measured Time, the symmetry of which is plain from the experiential equivalence of 'take less time' and 'cover more ground' as meanings of 'go faster'.  The representation of that ratio as a quotient, in turn, facilitates the further representation of it as part of a second quotient, i. e. in Velocity/Time.  So, that 'go faster' is easily comprehensible as an experiential concept only underscores that 'A = d/t-squared' is more contrived abstraction than insight.